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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.next_float.float_distance"></a><a class="link" href="float_distance.html" title="Calculating the Representation Distance Between Two floating-point Values (ULP) float_distance">Calculating the
      Representation Distance Between Two floating-point Values (ULP) float_distance</a>
</h3></div></div></div>
<p>
        Function float_distance finds the number of gaps/bits/ULP between any two
        floating-point values. If the significands of floating-point numbers are
        viewed as integers, then their difference is the number of ULP/gaps/bits
        different.
      </p>
<h5>
<a name="math_toolkit.next_float.float_distance.h0"></a>
        <span class="phrase"><a name="math_toolkit.next_float.float_distance.synopsis"></a></span><a class="link" href="float_distance.html#math_toolkit.next_float.float_distance.synopsis">Synopsis</a>
      </h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">next</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">FPT</span><span class="special">&gt;</span>
<span class="identifier">FPT</span> <span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">FPT</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">FPT</span> <span class="identifier">b</span><span class="special">);</span>

<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<h5>
<a name="math_toolkit.next_float.float_distance.h1"></a>
        <span class="phrase"><a name="math_toolkit.next_float.float_distance.description_float_distance"></a></span><a class="link" href="float_distance.html#math_toolkit.next_float.float_distance.description_float_distance">Description
        - float_distance</a>
      </h5>
<p>
        Returns the distance between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>:
        the result is always a signed integer value (stored in floating-point type
        FPT) representing the number of distinct representations between <span class="emphasis"><em>a</em></span>
        and <span class="emphasis"><em>b</em></span>.
      </p>
<p>
        Note that
      </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
            <code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
            always returns 0.
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_next</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
            always returns -1.
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="identifier">float_distance</span><span class="special">(</span><span class="identifier">float_prior</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">a</span><span class="special">)</span></code>
            always returns 1.
          </li>
</ul></div>
<p>
        The function <code class="computeroutput"><span class="identifier">float_distance</span></code>
        is equivalent to calculating the number of ULP (Units in the Last Place)
        between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> except that it
        returns a signed value indicating whether <code class="computeroutput"><span class="identifier">a</span>
        <span class="special">&gt;</span> <span class="identifier">b</span></code>
        or not.
      </p>
<p>
        If the distance is too great then it may not be able to be represented as
        an exact integer by type FPT, but in practice this is unlikely to be a issue.
      </p>
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